Special transforms of the generalized bivariate Fibonacci and Lucas polynomials

Abstract

This paper deals with the Catalan, Hankel, binomial transforms of the generalized bivariate Fibonacci and Lucas polynomials. Also, some useful results such as generating functions, Binet formulas, summations of transforms defined by using recurrence relations of these special polynomials are presented. Furthermore, certain important relations among these transforms are deduced by using obtained new formulas. Finally, the Catalan, Cassini, Vajda and d'Ocagne formulas for these transforms are also derived.

Keywords

• binomial transform
• bivariate Fibonacci polynomials
• Catalan transform
• Hankel transform
• Horadam polynomials

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